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Kainulainen, Mikko; McMullen, Jake; Lehtinen, Erno – Cognition and Instruction, 2017
Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…
Descriptors: Numbers, Foreign Countries, Grade 3, Grade 4
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Ding, Meixia; Li, Xiaobao – Cognition and Instruction, 2010
This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…
Descriptors: Comparative Analysis, Mathematics Education, Textbooks, Elementary School Mathematics
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Vamvakoussi, Xenia; Vosniadou, Stella – Cognition and Instruction, 2010
We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…
Descriptors: Secondary School Students, Intervals, Numbers, Mathematics
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Li, Xiaobao; Ding, Meixia; Capraro, Mary Margaret; Capraro, Robert M. – Cognition and Instruction, 2008
This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…
Descriptors: Foreign Countries, Comparative Analysis, Symbols (Mathematics), Grade 6
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Perry, Michelle – Cognition and Instruction, 2000
Documented differences in frequency and type of mathematical explanations during lessons in U.S., Taiwanese, and Japanese first- and fifth-grade classrooms. Found that explanations occurred more frequently in Japanese and Taiwanese classrooms than in U.S. classrooms. Typical explanations in Asian classrooms were more substantive than in U.S.…
Descriptors: Age Differences, Comparative Analysis, Cross Cultural Studies, Cultural Differences